Fourier Transform,
Damped(decaying) Exponent
Cuthbert Nyack
The damped Exponent is given by the expression below.
Its Fourier Transform can be readily found and is:-
The Applat below shows the variation of the Fourier Transform
as the parameter "a" is varied. In the
applet, the damped Exponent is shown in purple. When FGain is 1,
the horizontal range
for t is from 0 to 10s. The vertical scale for f(t) is from0 t0 +2.
Frequency parameter is in units of radians/sec.
For the spectrum, the following applies:-
The origin is in the CENTER of the plot.
Magnitude of spectrum is in green.
With VGain = 1 Vertical scale for the spectrum is from -2 to +2.
Phase is in red.
Vertical axis for phase is from - p
to + p.
Real part(even) of spectrum is in orange
and Imaginary part(odd) in yellow.
With SGain = 1, the horizontal scale for frequency is from
-2.5rad/s to +2.5rad/s.
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COPYRIGHT © 1996 Cuthbert Nyack.